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Linear Algebra vector

  1. Jan 17, 2009 #1
    1. The problem statement, all variables and given/known data

    The line l passes through the point P=(1,-1,1) and has direction vector d=[2,3,-1]. Determine whether l and P are parallel, perpendicular, or neither to 2x+3y-z=1.

    2. Relevant equations
    n.p=n.x, cross product, dot product


    3. The attempt at a solution
    Would you just relate the direction vector, d, to the normal vector, n[2,3,-1] ?
     
  2. jcsd
  3. Jan 17, 2009 #2

    Dick

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    Yes, you would just relate the normal vector to the direction vector. How do they relate?
     
  4. Jan 17, 2009 #3
    they would be parallel because they are scalar multiples of one another (1 is the multiple) also the cross product would be zero indicating parallel vectors.
     
  5. Jan 17, 2009 #4

    Dick

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    That means that the NORMAL to the plane is parallel to the line. So what's the relation between the line and the plane?
     
  6. Jan 17, 2009 #5
    that they are perpendicular?
     
  7. Jan 17, 2009 #6

    Dick

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    Yes, they are.
     
  8. Jan 17, 2009 #7
    How would you prove that mathematically?
     
  9. Jan 17, 2009 #8

    Dick

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    What's to prove? The normal vector of the plane is parallel to the line. You proved that by showing they are scalar multiples or using the cross product. You're done.
     
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